1. Solve the following system of equations using Gaussian elimination: 2x 1 3y - 2 7 4x - y + 5 - 14 3x + 2y - 4z - 5 2. What is the geometric interpretation of a system of equations having no solution, one solution, and infinitely many solutions? 3. Solve the system of linear equations x-y+2=3 2cty - z=4 by finding the inverse of the coefficient matrix. 1. Define a linear combination. Given vectors # = (1, 2) and if = (3, 4), express the vector wl = (7, 10) as a linear combination of o and i. 5. Given the matrix A = (? ;)- compute the matrix product AAT. In linear algebra, the transpose of a matrix A is another matrix A created by any one of the following equivalent actions: . Reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain A", . Write the rows of A as the columns of A", . Write the columns of A as the rows of AT. If A = [asj] is an m x n matrix, then A" = [o;] is an n x m matrix. 6. Define what it means for a set of vectors to be linearly independent. Determine whether the following vectors are linearly independent: 7. Define the span of a set of vectors. What is the span of the vectors v = (1, 0) and a = (0, 1)7 8. Given the matrix A = . solve the equation AF = 6. 9. Compute the matrix product of AB where A = (1 8 ) and # - ( 9)-10. Define a matrix transformation 7(3) = AZ, where A is a given matrix. Describe the effect of this transformation on the input space. 11. Given the matrix A = (3 2) find the inverse of A. 12. Consider the following matrix A = Compute the matrix 24 - 34, where A' is the transpose of matrix A